I have been playing bass trombone for about a year, and my problem is not positions or intonation, or air, but how to get a good big band (jazz band) bass trombone sound? I mean I listen to jazz bass trombonists both solo and within bands. And they have a specific tone, that's blattier than say a bass trombone in a concert band or orchestra setting. Any tips would be apreciated
Use a shallower mouthpiece. On any brass instrument, a shallower cup on the mouthpiece will allow the player more range (it's easier to switch partials; I'm actually not sure why, but I think it has to do with adding backpressure), but the tradeoff is a "blattier" sound; less mellow, harder to blend in with a large group (because that backpressure makes it easier to "overblow" the instrument), so classical teachers will encourage a deeper cup. Definitely avoid the long cone-shaped "mellophone-style" mouthpieces if you're looking for blat.
Also, try closing your mouth/soft palate a bit. If you've been trained in "singer-style" breath control (where you control the breath with your diaphragm, not by closing off your throat), you get a very nice open sound that's exactly what your classical brass teacher wants. But, your jazz teacher may actually tell you to clamp down a bit for stylistic purposes. Just don't totally forget the good habits of classical technique.
When I play I have trained myself to use a lot of air. I know you said air wasn't this issue but it really is. Get to a point where you edge out your horn and feel too blatty. Back off a bit, but you're going to feel blatty. It's not a very welcome feeling when playing brass because we're trained to not be blatty, but that's the sound you want. Get yourself a pretty big mouthpiece, I recommend a schilke 52, and learn to edge out. The bigger mouthpiece makes it harder to edge out meaning that you can get more volume with edging out. Learn to follow the thin line between blatty and weak. Think words like "edgey" or "meaty". And start out with getting a really solid low f. Don't be afraid to just pump air into the horn.
Side note: try articulating with a "th" syllable. It will create a great starting backbone for the note to follow.
Side side note: open your throat more. The sound should start around your larynx and it might tickle a little. That gives you a super full core of the note. Try different mouthpieces too.
Listen to as many good bass trombonists as you can. I recommend listening to Martin van den Berg playing Saturday Night. Here's the link: